The man who claims that "Starfleet is not a military organization" is the Captain of a spacecraft whose crew includes several hundred civilians, many of them children. This does not appear to be a feature unique to galaxy-class starships, since several years later we see this is also true of the USS Saratoga.

This is like saying that military bases adjacent to a neighborhood built specifically for the soldiers and their families isn't really military because of that fact, or is somehow fundamentally different from a base without said neighborhood.

Are you suggesting the original Enterprise had children and families on board during TOS?

Why don't you question what I said rather than your straw construct of my argument ?